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The Mathematics Education into the 21st Century Project

niversiti Teknologi Malaysia

Proceedings of the Eighth International Conference

Reform, Revolution and Paradigm Shifts in Mathematics Education


Alan Rogerson

Hotel Eden Garden, Johor Bahru, Malaysia

Nov 25th – Dec 1st 2005

Major Sponsors


All Rights Reserved.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright holder.

The Mathematics Education into the 21st Century Project wishes to thank for their support


RIC Publications


QED Education Scientific Pte Ltd

Statworks (M) Sdn Bhd

Texas Instruments

VSG Enrichment


Greygum Software

The Third World Forum

The Hong Kong Institute of Education

ALMA (Teacher Training Centre, Poland)

ISBN Number 83-919465-7-6

Conference Committees

International Program Committee


Dr. Alan Rogerson, International Coordinator of the Mathematics in Society Project

Prof Khaled Abuloum, University of Jordan (Jordan).

Professor Roberto Baldino, UNESP (Brazil).

Dr. Andy Begg , Senior Lecturer in Mathematics Education, University of Waikato (New Zealand).

Dr. Donna F. Berlin, Mathematics, Science & Technology Education, Ohio State University (USA)

Prof. Dr. Werner Blum, University of Kassel (Germany).

Professor Ubiratan D'Ambrosio, Emeritus Professor of Mathematics, Campinas/UNICAMP, (Brazil).

Professor Bruno D'Amore, University of Bolgna (Italy).

Professor Dr. Tilak de Alwis, Southeastern Louisiana University (USA)
Prof Dr William Ebeid, Emeritus Professor, Faculty of Education, Ain Shams University (Egypt).

Prof. Omar Hassan El Sheikh, University of Jordan (Jordan).

Professor Paul Ernest, University of Exeter (UK).

Prof. Dr. Gabriele Kaiser, Hamburg University (Germany).

Dr. Madeleine J. Long, Program Director, American Association for the Advancement of Science

Prof Dr Fayez Mina, Faculty of Education, Ain Shams University (Egypt).

Prof Nicolina Malara, University of Modena (Italy)

Prof Dr M. Ali M. Nassar, Director of Planning Center, Institute of National Planning (Egypt).

Professor Lionel Pereira Mendoza, Associate Professor, National Institute of Education (Singapore).

Professor Angela Pesci, University of Pavia (Italy)

Prof. Medhat Rahim, Lakehead University, Faculty of Education (Canada).

Professor Filippo Spagnolo, University of Palermo, Sicily, (Italy).

Professor Dr. Alicia Villar Icasuriaga, Instituto de Profesores "Artigas", Montevideo, (Uruguay)

Dr. Arthur L. White, Mathematics, Science, and Technology Education, Ohio State University (USA)

Professor. Wacek Zawadowski, Warsaw University (Poland).

^ Local Organizing Committee


Prof. Dr. Noor Azlan Ahmad Zanzali, Faculty of Education, Universiti Teknologi Malaysia

Associate Prof. Dr. Md. Nor Bakar
Associate Prof. Dr. Zaleha Ismail
Associate Prof. Dr. Mohini Mohamed
Associate Professor Aziz Nordin

Dr. Zaidatun Tasir
En. Asram Sulaiman @ Saim
Puan Sumi Hj. Isman
En. Bahrim Kasim


This volume contains the papers presented at the International Conference on Reform, Revolution and Paradigm Shifts in Mathematics Education held from November 25 to December 1st, 2005 at the Hotel Eden Garden, Johor Bahru, Malaysia. This Conference was organized jointly by Universiti Teknologi Malaysia and The Mathematics Education into the 21st Century Project - a non-commercial international educational project founded in 1986. Our Project is dedicated to the improvement of mathematics education worldwide through the publication and dissemination of innovative materials and ideas.

The title Reform, Revolution and Paradigm Shifts in Mathematics Education derives from Kuhn's seminal work on "The Structure of Scientific Revolutions" which made popular the concept of "paradigm shift", and the work of Lakatos which revealed the essentially creative and human nature of progress in science and mathematics. We hope these powerful ideas will help to inspire our conference.

The Mathematics Education into the 21st Century Project is dedicated to the improvement of mathematics education world-wide through the publication and dissemination of innovative ideas. Many prominent mathematics educators have supported and contributed to the project, including the late Hans Freudental, Andrejs Dunkels and Hilary Shuard, as well as Bruce Meserve and Marilyn Suydam, Alan Osborne and Margaret Kasten, Mogens Niss, Tibor Nemetz, Ubi D’Ambrosio, Brian Wilson, Tatsuro Miwa, Henry Pollack, Werner Blum, Roberto Baldino, Waclaw Zawadowski, and many others throughout the world. Information on our project and its future work can be found on the following webpages. - Malaysia 2005 Conference - Our Project Home Page - Egypt Conference site - Jordan conference site - Australia conference site - Sicily Conference site - Brno Conference site - Ciechocinek Conference site

Filippo Spagnolo, of Palermo University, is webmaster for the above sites. Felix Rieper has some photos of the Ciechocinek Conference:

Krys Bestry is webmaster for our Polish Superkurs Home Page at (in Polish - but with pictures!) See also: and for more information about our project and its work.

It has been my pleasure to read all of the papers and to edit them for these Proceedings. Not all papers are about research in mathematics education, a number report on innovative experiences in the classroom and on new technology. We believe that “mathematics education” is fundamentally a “practicum” and so in order to be “successful” all new materials, new ideas and new research must be tested and implemented in the classroom, the real “chalk face” of our discipline, and of our profession as mathematics educators .

These Proceedings begin with two commissioned papers and otherwise contain contributions mostly in alphabetical order of the Principal Presenters. I sincerely thank all of the contributors for their time and creative effort. It is clear from the variety and quality of the papers that the conference has attracted many innovative mathematics educators from around the world. These Proceedings will therefore be useful in reviewing past work and looking ahead to the future. For further information about the work of our Project, please email

Dr. Alan Rogerson

Chaiman of the Programme Committee


Presented Papers

Comparing mathematics education traditions in four European countries: The

case of the teaching of percentages in the primary school

Erik De Corte, Fien Depaepe, Peter Op ’T Eynde & Lieven Verschaffel .......1

Cultural differences in scholastic and non-scholastic environments: reasoning

patterns and logical-linguistic questions in European and Chinese cultures

Maria Ajello, Filippo Spagnolo, Zhang Xiaogui .....12

Learning with Examples and Students’ Understanding of Integration

Shafia Abdul-Rahman .....24

Share the Experience! Problem-Solving is No Longer a Problem.

Fadia Abou Najem .....29

Teachers’ competency in the teaching of mathematics in English in Malaysian

secondary schools

Hamidah Ab Rahman, Aziz Nordin, Mukheta Isa, Fatimah Puteh, et al. .....31

Students Problem Solving Processes in LOGO Programming Environment Pengaturcaran LOGO

Suguna Appalanayudu, Zaleha Ismail .....37

Dynamic Worksheets – a Tool for Individual and Cooperative Learning

Peter Baptist .....41

Mathematics education in Finland – what makes it work?

Ole Bjorkqvist .....45

Thinking mathematically – making sense and solving problems

George Booker .....49

Enhancement of Teaching Policy by means of Technology

Hennie Boshoff .....54

Curriculum Issues in Statistics Education

Gail Burrill .....59

^ The mathematics allergy: Is Drama in Education the much-needed antidote?

Carol Carter and Lise Westaway .....65

Emphasis on Problem Solving in Mathematics Textbooks from Two Different

Reform Movements

Jaguthsing Dindyal .....70

Early School Leavers Experiences Of Learning Mathematics: The Discourses

Of Mathematics Classrooms

Bronwyn Ewing .....75

The Two Fundamental Learning Games We Play: A Framework For

Discussion And Reflection

Gary Flewelling .....81

Introducing the Least Squares Regression Principle with Computer Technologies

Patricia A Forster .....87

SEARCHING for control in a post-modern mathematics classroom.

Noel Geoghegan .....92

Dominant Representation In The Understanding Of Basic Integrals Among Post Secondary Students

Munirah Ghazali, Siti Aishah Sheikh Abdullah, Zurida Ismail, Mohd Irwan Idris .....97

The Role of Professional Development Networks in Reforming Mathematics

Education in Egypt

Amal Gouda & Frank Banks ...101

Elementary Mathematics Pre-Service Teachers’ Learning from Cases

Marjorie Henningsen ...106

Conceptests: Active Learning In Calculus

Deborah Hughes Hallett, Maria Robinson, David Lomen ...112

The Mathematics Carnival: A Platform to Appreciate Mathematics

Zaleha Ismail, Mohd Khalid Kasmin & Norma Alias ...115

Mathematics textbooks – the link between the intended and the implemented curriculum?

Monica Johansson ...119

Inservice and Preservice Teachers’ Attitudes Regarding the Use of Graphing Calculators to Support Inquiry Learning in Mathematics

Iris Johnson ...124

Paper Folding Squares

Kwan Shi-pui & Sze Chong-lap ...129

^ Promoting Mathematics Teacher Collaboration through Lesson Study: What Can We Learn from Two Countries’ Experience?

Lim Chap Sam, Allan Leslie White & Chiew Chin Mon ...135

Recruiting, Educating, and Retaining Teachers of Mathematics

Madeleine J. Long ...140

Developing mathematical thinking with the assistance of manipulatives

Linda Marshall & Paul Swan ...144

Using Autobiography To Change Preservice Teachers’ Attitudes Towards Mathematics

Keith McNaught ...148

Reform, Revolution and Paradigm Shifts in Mathematics Education. Some

^ Examples and Applicable Strategies

Fayez M. Mina ...154

The Use Of Metacognitive Process In Learning Mathematics

Mohini Mohamed & Tan Ten Nai ...159

An Evaluative Study to Pre-service Primary Teachers in Mathematics in Egypt

Ayman Moustafa Moustafa ...163

Enriching math teaching by computers

Marjatta Näätänen ...169

Innovative and Technology Based Methods of Teaching Statistics Concepts

Mehryar Nooriafshar ...172

Teaching Mathematics: Tablet PC Technology adds a new dimension

Werner Olivier ...176

New Possibilities in Analysis using the ClassPad300Plus

Ludwig Paditz ...182

Identifying mentoring practices for developing effective primary mathematics teaching

Peter Hudson and Robert Peard ...189

Math Anxiety in Junior/Intermediate Pre-Service Teachers

Medhat H. Rahim & Matthew Koeslag ...194

Making the most of games: Lesson learned from playing Numero

Paul Swan & Linda Marshall. ...199

Preparing Teachers to Teach Mathematics to Students with Learning Disabilities

Tony Thompson ...204

Misconceptions And Difficulties With The Chain Rule

Tangül Uygur & Aynur Özdaş ...209

Paradigm Shift in Mathematics Education from 'Traditional’ Learning Method to Modified Climbing Learning Method: Its Applicability and Effectiveness in Kenyan Secondary School

Nancy Nui Wambui ...214

“Masifunde Nosapho” (“Let us learn with our families”)

Lise Westaway & Carol Carter ...218

^ Workshop Presentations & Short Abstracts

Mathematica© As a Tool For Exploring Mathematics

Mohamad Faisal Abdul Karim ...223

Secondary Students Scheme of Composite Functions

Siti Aishah Sh.Abdullah & Fatimah Saleh ...224

Teaching about Islamic Art/Learning Geometry, Teaching Geometry/Learning

about Islamic Art

Carol Bier ...224

Using games to develop conceptual understanding in order to analyse problem meanings and devise problem solutions

George Booker ...227

^ Teacher-student cooperation
Josephine Buskes ...227

Pure and applied mathematics –what is the driving force in curriculum in different countries – and what about the interaction between pure and applied mathematics?

Liv Sissel Grønmo ...227

Doing mathematics is not only solving set problems given by others, but also (and especially) creating new problems and asking good questions

Jean Michel Hanna ...228

Wholemovement of Folding Circles

Bradford Hansen-Smith ...230

Mathematical Experiences in a Technology Integration Research Study

Mhairi (Vi) Maeers ...230

Using An Interactive Whiteboard In The Mathematics Classroom. A workshop for practitioners and educators

Dave Miller and Doug Averis ...231

Being Mathematical: New Questions for Old

^ Yudariah Mohd. Yusof and Roselainy Abdul Rahman ...231

Invoking Students’ Use of their Own Powers of Mathematical Thinking Workshop

Yudariah Mohd. Yusof & Roselainy Abdul Rahman. ...232

An Introduction to Dynamic Programming - The Two Hour Challenge

Mehryar Nooriafshar ...232

Stochastics/Simulation and Exploration with the new ClassPad300plus

Ludwig Paditz ...233

Autograph is a dynamic software which is effective, efficient and FUN for both teacher and student.

Cecily Peters ...236

Visualizing Algebra Using Dynamic Geometry® Software

Steve Rasmussen ...236

What Happens When…

Kerry J Thomas ...237

Images with maths

Rüdiger Vernay ...237

Integrating Constructivist approaches in e-learning to enhance mathematical self-study

Ya Ling Lee ...238

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